ALBANY - New York is moving toward establishing a statewide health-insurance exchange intended to extend coverage to the uninsured and reduce costs for individuals, small businesses and local governments.

The New York Health Benefit Exchange, a federally required and subsidized marketplace for buyers, was established by Gov. Cuomo by executive order last April.

New York has an estimated 2.7 million uninsured among roughly 19 million residents, said Danielle Holahan, director of policy and planning for the Health Department’s exchange.

WASHINGTON - Georgia, Ohio and Wisconsin joined more than a dozen other states on Friday in saying they would not establish health insurance exchanges, while a handful of other states said they would take advantage of an extra month allowed by the Obama administration to make decisions.

The exchanges - online markets where consumers can shop for private insurance subsidized by the federal government - are a centerpiece of President Obama's health care law.

The administration has been urging states to set up exchanges, as Congress intended. The federal government will create and run exchanges in any state that is unable or unwilling to do so.

Mr. Obama and his health secretary, Kathleen Sebelius, have promised to give states flexibility in carrying out the new health care law and running the exchanges. However, Republican governors said they had not been allowed much latitude to date.

Gov. John R. Kasich of Ohio, a Republican, said Friday that his state "will not run an Obamacare health exchange, but will instead leave that to the federal government to do."

"Based on the information we have," Mr. Kasich said, "states do not have any flexibility to build and manage exchanges in ways that respond to unique needs of their citizens."

Gov. Scott Walker of Wisconsin, another Republican opposed to the health care law, said, "From a philosophical standpoint, I prefer state-run over federal on any day on any subject." But under the law, Mr. Walker said, "Wisconsin taxpayers will not have meaningful control over the health care policies and services sold to Wisconsin residents."

For decades, under governors of both parties, Wisconsin has been a national leader in the regulation of insurance.

Caroline F. Pearson, who tracks state developments at Avalere Health, a consulting company in Washington, said it appeared that about 18 states would choose to run their own exchanges, while 10 to 12 would seek partnerships with the federal government, and 18 to 20 would have federal exchanges.

Friday was to be the deadline for states to declare their intentions. But Ms. Sebelius said Thursday night that she was extending the deadline to Dec. 14. In any event, she must decide by Jan. 1 whether states are able to run their own exchanges.

Americans are supposed to be able to start shopping for insurance through exchanges in October 2013. By January 2014, most Americans will be required to have health insurance under the law.

Obama administration officials said they would be ready to run the federal exchanges, but they have not provided any information about their plans or their progress.

Gov. Rick Scott of Florida, a Republican, asked Friday for a meeting with Ms. Sebelius to discuss plans for an exchange. He said he was still analyzing his options, but had not seen evidence that an exchange would lower health costs for Floridians.

Gov. Nathan Deal of Georgia, a Republican, said his state would not establish an exchange. He expressed concern about what he described as "the one-size-fits-all approach and high federal burden imposed on states."

Other Republican governors, including Jan Brewer of Arizona, C. L. Otter of Idaho, Terry E. Branstad of Iowa, Chris Christie of New Jersey, Tom Corbett of Pennsylvania and Bill Haslam of Tennessee, said they would use the extra time to seek more answers from Washington and feedback from constituents.

In a letter to Ms. Sebelius, Mr. Branstad said his state wanted to create its own exchange, but needed much more information. He included a list of 50 questions and said that unless they were answered, Iowa might have no choice but to opt for a federal exchange.

Many of the questions were about the costs of building and running an exchange. Mr. Otter said he would consult leaders of the Idaho Legislature and make a decision by the new deadline. An advisory committee appointed by Mr. Otter recommended last month that Idaho create its own exchange. But, Mr. Otter said, "I don't want us buying a pig in a poke."

Gov. Bev Perdue of North Carolina, a Democrat, said her state intended to join the federal government in establishing a hybrid form of exchange. Ms. Perdue will soon be succeeded by Pat McCrory, a Republican, who will decide what role the state should play.

Heather H. Howard, a lecturer at Princeton University who provides technical help to states as director of the State Health Reform Assistance Network, said the guidance provided by the Obama administration was sufficient for states to make decisions. States like California, Maryland and Washington have made great strides in developing exchanges, she said.

Ms. Howard said that governors might try to use the extra time to negotiate. "They're feeling their oats and testing the limits of what leverage they have," she said.